(4v+12)(v+7)=0

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Solution for (4v+12)(v+7)=0 equation: 


Simplifying
(4v + 12)(v + 7) = 0

Reorder the terms:
(12 + 4v)(v + 7) = 0

Reorder the terms:
(12 + 4v)(7 + v) = 0

Multiply (12 + 4v) * (7 + v)
(12(7 + v) + 4v * (7 + v)) = 0
((7 * 12 + v * 12) + 4v * (7 + v)) = 0
((84 + 12v) + 4v * (7 + v)) = 0
(84 + 12v + (7 * 4v + v * 4v)) = 0
(84 + 12v + (28v + 4v2)) = 0

Combine like terms: 12v + 28v = 40v
(84 + 40v + 4v2) = 0

Solving
84 + 40v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + 10v + v2) = 0

Factor a trinomial.
4((7 + v)(3 + v)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + v)' equal to zero and attempt to solve:

Simplifying
7 + v = 0

Solving
7 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + v = 0 + -7
v = 0 + -7

Combine like terms: 0 + -7 = -7
v = -7

Simplifying
v = -7

Subproblem 2
Set the factor '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

Solving
3 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + v = 0 + -3
v = 0 + -3

Combine like terms: 0 + -3 = -3
v = -3

Simplifying
v = -3
Solution
v = {-7, -3}

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